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BITSAT2022MathematicsArea Under CurvesActual

The area of the region bounded by the parabola (y-2)^2=(x-1) , the tangent to the parabola at the point (2,3) and the X -axis is

Options

  1. A3
  2. B6
  3. C9
  4. D12

Correct answer

C. 9

Step-by-step solution

The equation of the parabola is y^2-4 y-x+5=0 The equation of tangent at (2,3) is aligned 3 y-2(y+3)- x+2 2 +5 & =0 2 y-x-4 & =0 aligned Required area A is given by aligned & A= ₀^3 (x₂-x₁ ) d y & A= ₀^3 [ (y-2)^2+1 - 2 y-4 ] d y & A= ₀^3 (y^2-6 y+9 ) d y= ₀^3(3-y)^2 d y & =- [ (3-y)^3 3 ]₀^3=9 & aligned

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